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EXAMPLE
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To generate the array, start with all 1's in row 0; from then on,
obtain row n+1 from row n by first removing terms in row n at
positions 0 and {(m+1)*(m+2)/2-2,m>0} and then taking partial sums.
This square array A begins:
(1), (1), 1, 1, (1), 1, 1, 1, (1), 1, 1, 1, 1, (1), 1, 1, 1, 1, 1, ...;
(1), (2), 3, 4, (5), 6, 7, 8, (9), 10, 11, 12, 13, (14), 15, 16, ...;
(3), (7), 13, 20, (28), 38, 49, 61, (74), 89, 105, 122, 140, (159),...;
(13), (33), 71, 120, (181), 270, 375, 497, (637), 817, 1019, 1244, ...;
(71), (191), 461, 836, (1333), 2150, 3169, 4413, (5906), 8001, ...;
(461), (1297), 3447, 6616, (11029), 19030, 29483, 42775, (59324),...;
(3447), (10063), 29093, 58576, (101351), 185674, 300329, 451277, ...;
(29093), (87669), 273343, 573672, (1024949), 1982310, 3330651, ...;
(273343), (847015), 2829325, 6159976, (11320359), 23009602, 39998897, ...;
where terms in parenthesis at positions {0,1,4,8,13,..} in a row
are removed before taking partial sums to obtain the next row.
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RELATION TO SPECIAL TRIANGLE.
Triangle A104980 begins:
1;
1, 1;
3, 2, 1;
13, 7, 3, 1;
71, 33, 13, 4, 1;
461, 191, 71, 21, 5, 1;
3447, 1297, 461, 133, 31, 6, 1;
29093, 10063, 3447, 977, 225, 43, 7, 1; ...
in which column 0 and column 1 are found in square array A.
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Matrix square of A104980 = triangle A104988 which begins:
1;
2, 1;
8, 4, 1;
42, 20, 6, 1;
266, 120, 38, 8, 1;
1954, 836, 270, 62, 10, 1;
16270, 6616, 2150, 516, 92, 12, 1;
151218, 58576, 19030, 4688, 882, 128, 14, 1; ...
where column 1 and column 2 are also found in square array A.
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